hw1-sol

hw1-sol - MAE 143A Homework 1 Solutions 34. e) g(t) =...

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Unformatted text preview: MAE 143A Homework 1 Solutions 34. e) g(t) = 5e(-t/4)u(t) 5 4 g(t) 3 2 1 0 -5 -4 -3 -2 -1 0 t 1 2 3 4 5 f) g(t) = rect(t)cos(2*pi*t) 1 g(t) 0.5 0 -0.5 -1 -1.5 -1 -0.5 0 t 0.5 1 1.5 0.5 1 1.5 g) g(t) = -6rect(t)cos(3*pi*t) 6 4 g(t) 2 0 -2 -4 -6 -1.5 -1 -0.5 0 t 0 2 a) sin π t 6 5 2 ,2 6e , 2 2 b) g(t) 0 g(t) -2 -4 -6 -8 -10 -8 -6 -4 -2 0 t c) g(2t) 2 4 6 8 10 -8 -6 -4 -2 0 t 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 0 g(t) -2 -4 -6 -8 -10 d) 2g(3-t) 0 g(t) -5 -10 -15 -10 -8 -6 -4 -2 0 t e) -2g((t+1)/2) 15 10 g(t) 36. , ,5 10 5 0 -10 -8 -6 -4 -2 0 t . 5 38. . 15 ∑∞ a) 15 b) 42. . 5 . 15 ∑∞ 4 4 45. a) g(2t) g(t) 2 0 -2 -3 -2 -1 0 1 2 3 4 5 6 t a) -3g(-t) 5 g(t) 0 -5 -10 -6 -4 -2 0 t b) g(t+4) 2 4 6 g(t) 2 0 -2 -3 -2 -1 0 1 g(t) 5 2 t -2g((t-1)/2) 3 4 5 6 7 0 -5 -4 -2 0 2 t 4 6 8 58. Even 1.2 1 x(t) 0.8 0.6 0.4 0.2 0 -0.2 -5 -4 -3 -2 -1 0 t 1 2 3 4 5 1 2 3 4 5 Odd 1 x(t) 0.5 0 -0.5 -1 -5 59. -4 -3 -2 28 sin 400 d) -1 12 cos 500 Periodic 0.02 (LCM) 10 sin 5 e) 4 cos 7 Periodic 2 (LCM) 0 t 4 sin 3 f) 3 sin √3 Not periodic 60. 2 a) ∞ ∞ 2 4 1 4 8 b) ∞ 8 ∞ 1 1 8 3 c) ∞ 3 ∞ 9 36 1 4 ...
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This note was uploaded on 01/15/2012 for the course MAE 143A taught by Professor Miroslavkrstic during the Summer '08 term at UCSD.

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